Hitherto, there has been proposed a lubricating oil supply device of this type, in which oil leaked from a regulator, which is a part of oil discharged from a hydraulic pump, is supplied to an object to be lubricated of an automatic transmission and an oil cooler (see Patent Document 1, for example). The device includes a lubrication pressure regulator that regulates a pressure (lubrication pressure) to be supplied to the object to be lubricated and that supplies the leaked oil to the oil cooler, and the lubrication pressure regulator is driven by a dedicated electromagnetic valve. Specifically, the electromagnetic valve is controlled such that the amount of oil to be supplied to the object to be lubricated is reduced and the amount of oil to be supplied to the oil cooler is increased in the case where the vehicle speed is equal to or more than a predetermined vehicle speed (high-speed travel) and the engine load is equal to or less than a predetermined value (low load).